A #3 copper wire with an insulation factor of 75 and 90 degrees C is rated at 100 and 105 amps respectively.
A 100 amp service requires that you use AWG 4 copper wire or AWG 2 aluminum wire.
Service entrance wire size is AWG # 3 copper.
A 100 amp residential service requires a size #8 copper wire, it should be insulated in green.
The minimum size grounding conductor for a 100 amp service is a #8 bare copper wire.
2 AWG Aluminum for 100 Amp Service.
Service wire for 100 amps requires AWG #3 copper.
4 AWG
SE #2
Service entrance wire must be AWG # 4 Copper wire.
#2 wire copper
A#3 bare copper conductor is used for a ground wire for 100 amp service.
I would recommend you use AWG # 2 copper or AWG # 1/0 aluminum for that distance and amperage.